arXiv subjects

M. L. N. Goncalves

Publications and source records attributed to M. L. N. Goncalves.

8 recordsLinked to original sources

arXiv2017

An Inexact Newton-like conditional gradient method for constrained nonlinear systems

In this paper, we propose an inexact Newton-like conditional gradient method for solving constrained systems of nonlinear equations. The local convergence of the new method as well as results on its rate are established by using a general majorant condition. Two applications of such condition are provided: one is for functions whose the derivative satisfies Holder-like condition and the other is for functions that satisfies a Smale condition, which includes a substantial class of analytic functions. Some preliminaries numerical experiments illustrating the applicability of the proposed method for medium and large problems are also presented.

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arXiv2017

Iteration-complexity analysis of a generalized alternating direction method of multipliers

This paper analyzes the iteration-complexity of a generalized alternating direction method of multipliers (G-ADMM) for solving linearly constrained convex problems. This ADMM variant, which was first proposed by Bertsekas and Eckstein, introduces a relaxation parameter $α\in (0,2)$ into the second ADMM subproblem. Our approach is to show that the G-ADMM is an instance of a hybrid proximal extragradient framework with some special properties, and, as a by product, we obtain ergodic iteration-complexity for the G-ADMM with $α\in (0,2]$, improving and complementing related results in the literature. Additionally, we also present pointwise iteration-complexity for the G-ADMM.

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arXiv2017

On the pointwise iteration-complexity of a dynamic regularized ADMM with over-relaxation stepsize

In this paper, we extend the improved pointwise iteration-complexity result of a dynamic regularized alternating direction method of multipliers (ADMM) for a new stepsize domain. In this complexity analysis, the stepsize parameter can even be chosen in the interval $(0,2)$ instead of interval $(0,(1+\sqrt{5})/2)$. As usual, our analysis is established by interpreting this ADMM variant as an instance of a hybrid proximal extragradient framework applied to a specific monotone inclusion problem.

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arXiv2014

Local convergence of inexact Gauss-Newton like methods for injective-overdetermined systems of equations under a majorant condition

In this paper, inexact Gauss-Newton like methods for solving injective-overdetermined systems of equations are studied. We use a majorant condition, defined by a function whose derivative is not necessarily convex, to extend and improve several existing results on the local convergence of the Gauss-Newton methods.In particular, this analysis guarantees the convergence of the methods for two important new cases.

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arXiv2013

Local convergence analysis of a proximal Gauss-Newton method under a majorant condition

In this paper, the proximal Gauss-Newton method for solving penalized nonlinear least squares problems is studied. A local convergence analysis is obtained under the assumption that the derivative of the function associated with the penalized least square problem satisfies a majorant condition. Our analysis provides a clear relationship between the majorant function and the function associated with the penalized least squares problem. The convergence for two important special cases is also derived.

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arXiv2010

Local convergence analysis of inexact Gauss-Newton like methods under majorant condition

In this paper, we present a local convergence analysis of inexact Gauss-Newton like methods for solving nonlinear least squares problems. Under the hypothesis that the derivative of the function associated with the least square problem satisfies a majorant condition, we obtain that the method is well-defined and converges. Our analysis provides a clear relationship between the majorant function and the function associated with the least square problem. It also allows us to obtain an estimate of convergence ball for inexact Gauss-Newton like methods and some important, special cases.

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arXiv2010

Local convergence analysis of Gauss-Newton's method under majorant condition

The Gauss-Newton's method for solving nonlinear least squares problems is studied in this paper. Under the hypothesis that the derivative of the function associated with the least square problem satisfies a majorant condition, a local convergence analysis is presented. This analysis allow us to obtain the optimal convergence radius, the biggest range for the uniqueness of solution, and to unify two previous and unrelated results.

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arXiv2008

Local convergence analysis of inexact Newton-like methods under majorant condition

We present a local convergence analysis of inexact Newton-like methods for solving nonlinear equations under majorant conditions. This analysis provides an estimate of the convergence radius and a clear relationship between the majorant function, which relaxes the Lipschitz continuity of the derivative, and the nonlinear operator under consideration. It also allow us to obtain some important special cases

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